Simplify the following expression: $y = \dfrac{q^2 - 13q + 30}{q - 10} $
Solution: First factor the polynomial in the numerator. $ q^2 - 13q + 30 = (q - 10)(q - 3) $ So we can rewrite the expression as: $y = \dfrac{(q - 10)(q - 3)}{q - 10} $ We can divide the numerator and denominator by $(q - 10)$ on condition that $q \neq 10$ Therefore $y = q - 3; q \neq 10$